Follow UT Dallas:

Professor John Zweck's Research Melds Math With Other Fields

Dr. John Zweck joined the Department of Mathematical Sciences last year.

Combining mathematics and computation with nearly any other field yields a wealth of possibilities, says a UT Dallas mathematics professor whose research tends to gravitate toward such intersections.

Dr. John Zweck, a professor in the Department of Mathematical Sciences who joined the faculty last year, earned his bachelor’s degree from the University of Adelaide in Australia and his PhD in mathematics from Rice University. His training concentrated on differential geometry, which involves understanding shapes in space.

“In the late 1990s, I made a radical switch from pure mathematics and turned myself into what I would call a mathematically sophisticated engineer,” Zweck said.

During several postdoctoral projects, he found himself immersed in research at the interface of computational and applied mathematics and engineering. Much of Zweck’s research involves optics, including optimizing systems that transmit large amounts of data over long distances through fiber optic cables.

“Nowadays, all long-distance telephone and Internet traffic travels through fiber optic cables,” Zweck said. “The digital data – the 1s and 0s – are encoded as pulses of light. If you were to cut a cable in half, you would see flashes going on and off. There are mathematical equations that govern this propagation of light through the fibers, and we use those equations to optimize the design to get more capacity – more pulses-per-second through the system while keeping the probability of errors low.”

Zweck’s work also has applications in high-performance lasers that operate using very rapid pulses of light.

PREVIOUSLY: Associate professor, University of Maryland, Baltimore County

“There are many applications for femtosecond lasers,” Zweck said. “One is to measure time and frequency extremely accurately, which is important for precision GPS navigation.”

The challenge researchers face, he said, is to develop mathematical models of engineering systems that are simple enough to be amenable to mathematical analysis, yet sophisticated enough to be useful for engineering design optimization.

“I see myself as someone who uses interdisciplinary computational and applied mathematics to help experimentalists and theoreticians in science and engineering solve problems that they can’t solve just by doing experiments or just by doing theory,” Zweck said. “Because of advances in computer science, we can connect theoretical mathematics with applications, and produce visualizations to better communicate with biologists, medical professionals and engineers of various stripes.”

Zweck has held academic positions at several institutions, and was an associate professor of mathematics and statistics at the University of Maryland, Baltimore County, before joining the UT Dallas faculty. Among the classes he teaches is undergraduate-level multivariable calculus.

“This is a very exciting time for students who are mathematically literate who also have an interest in science and computation,” Zweck said. “Based on my own experience, I have come to a much better understanding of how important it is for undergraduates to learn and understand multivariable calculus, and to apply geometric thinking to engineering problems in novel ways.

“I would encourage students who have an interest in math to go as far as they can with it, and look for opportunities to uncover intersections between math and other areas of science – they are everywhere.”